Narrow spectral linewidth of semiconductor (SC) lasers is of great importance for many applications, such as optical communication systems, interferometric fiber sensors, etc. The nature of most applications is such that a small monolithic device is desired, a property that may not always be accommodated with the narrow linewidth required. Like any other laser, a SC laser may operate in a number of longitudinal modes, which are the allowed frequencies dictated by the optical resonator. Since these lasers are normally very small (typically much less than 1 mm) the mode spacing is large, and optical methods such as grating feedback are used to select a single mode for the operation of the laser. Even a laser operating in a single longitudinal mode still possesses a finite linewidth, as determined by fundamental physical processes involved in the lasing action itself.
For any laser, the ultimate linewidth is determined by the Schawllow-Townes (ST) limit, which is a manifestation of the process of spontaneous emission as it affects the laser linewidth. In SC lasers the fundamental limit is higher, due to the very strong coupling between intensity and phase fluctuations in these lasers. According to the well established Henry theory [C. H. Henry, "Theory of the phase noise and power spectrum of a single mode injection laser", IEEE J. Quantum Electron. vol. QE-19, 1391-1397, (1983)] the lineshape and linewidth of a single-mode SC laser are defined by refractive index fluctuations, induced by the gain changes due to the fluctuations in the number of carriers. In SC lasers the dispersion curve of the refractive index is shifted from the gain-peak frequency, so that the change of the imaginary part of the susceptibility (gain) is accompanied by a corresponding change in its real part (refractive index) via the Kramers-Kronig relations. Both the gain and the refractive index depend on the carrier number, and carrier number fluctuations caused by spontaneous emission induce refractive index changes.
For Gaussian statistics of fluctuations, the field correlation function is EQU (E(t)E(0))=exp (-1/2(.PHI.(t).sup.2)) (1)
Where .PHI.(t) is the field phase. According to Henry, EQU (.PHI.(t).sup.2)=R/(2I)((1+.alpha..sup.2)t+.alpha..sup.2 /(2.GAMMA.)(1-exp (-.GAMMA.t) cos (.OMEGA.t))) (2)
Here, R is the spontaneous emission rate, I is the steady state photon number, .GAMMA. and .OMEGA. are the damping rate and the frequency of the relaxation oscillations (RO), .alpha. is the enhancement factor. The term in (2) which has linear dependence on time is connected with the long time fluctuations of the carrier number. The oscillating term is connected with the RO of the carrier number and of the intensity, which results from the return to steady state after perturbation. The linear term defines the linewidth. EQU .DELTA..omega.=R/(2I)(1+.alpha..sup.2) (3)
Where R/(2I) is the ST width. The parameter .alpha..sup.2 ranges in value between 5-50 for various type of lasers, so that a method by which the long time fluctuations of carrier number are suppressed provides a narrowing of linewidth by the same factor.
The most common approach to spectral line narrowing is based on optical feedback from an external cavity ("External optical feedback effects on semiconductor injection laser properties", R. Lang and K. Kobayashi, IEEE J. Quantum Electron. vol. QE-16, p. 347, 1980). Due to the improved quality factor attainable with external cavities, the coupling to an external cavity provides significant linewidth reduction and improved frequency stability ("Stable semiconductor laser with a 7-Hz linewidth by an optical-electrical double-feedback technique", C. H. Shin and M. Ohtsu, Opt. Lett. vol. 15, p. 1455, 1990). The realizations of this approach, however, requires a cavity outside the monolithic semiconductor device, and a resonator which is much larger and does not reside on the laser chip, a property not compatible with various applications.
In a SC laser, intensity noise results from the fluctuations in the number of carriers in the laser material, and several authors have studied the correlation between laser noise and carrier number fluctuations. It has been shown that the number of carriers, as well as the frequency and/or intensity fluctuations are strongly correlated to the junction voltage (JV), and indeed the junction voltage has been used for the purpose of stabilizing intensity and frequency noise in SC lasers ("Quantum correlation between the junction-voltage fluctuation and the photon-number fluctuation in a semiconductor laser", W. H. Richardson and Y. Yamamoto, Phys. Rev. Lett. vol 66, p. 1963, 1991; "Use of quantum-noise correlation for noise reduction in semiconductor lasers", A. Karlsson, and G. Bjork, Phys. Rev. A, vol. 44, p. 7669, 1991.). The correlation between JV noise and intensity or frequency noise in a two-section DBR semiconductor laser was measured, and stabilization possibilities were discussed. ("Measurements and theory of correlation between terminal electrical noise and optical noise in a two-section semiconductor laser", E. Goobar, A. Karlsson, and S. Machida, IEEE J. Quantum Electron. vol. 29, p. 386, 1993.).
It is also established that the phase and magnitude of the reflection from the surface of a semiconductor may be controlled accurately by an external voltage which is applied to a properly wired section near the face of the semiconductor ["Single-mode very wide tunability in laterally coupled semiconductor lasers with electrically controlled reflectivities", G. Griffel, H. Z. Chen, I. Grave, A. Yariv, Appl. Phys. Lett. vol. 58(17), p. 1827, 1991].
The above mentioned stabilization methods are capable of reducing excess frequency noise, and lowering the laser linewidth to the limit dictated by the Henry theory (the "Henry" linewidth) for single mode SC lasers. The externally stabilized lasers reach a limit much lower than the one derived from the Henry theory, but in most cases still higher than the ST limit. In addition, the external cavity stabilization is not acceptable for many applications because the obtained device is no longer monolithic, and the optical cavity is large and cumbersome.